Low degree metabolites explain essential reactions and enhance modularity in biological networks.

Recently there has been a lot of interest in identifying modules at the level of genetic and metabolic networks of organisms, as well as in identifying single genes and reactions that are essential for the organism. A goal of computational and systems biology is to go beyond identification towards an explanation of specific modules and essential genes and reactions in terms of specific structural or evolutionary constraints. In the metabolic networks of Escherichia coli, Saccharomyces cerevisiae and Staphylococcus aureus, we identified metabolites with a low degree of connectivity, particularly those that are produced and/or consumed in just a single reaction. Using flux balance analysis (FBA) we also determined reactions essential for growth in these metabolic networks. We find that most reactions identified as essential in these networks turn out to be those involving the production or consumption of low degree metabolites. Applying graph theoretic methods to these metabolic networks, we identified connected clusters of these low degree metabolites. The genes involved in several operons in E. coli are correctly predicted as those of enzymes catalyzing the reactions of these clusters. Furthermore, we find that larger sized clusters are over-represented in the real network and are analogous to a 'network motif. Using FBA for the above mentioned three organisms we independently identified clusters of reactions whose fluxes are perfectly correlated. We find that the composition of the latter 'functional clusters' is also largely explained in terms of clusters of low degree metabolites in each of these organisms. Our findings mean that most metabolic reactions that are essential can be tagged by one or more low degree metabolites. Those reactions are essential because they are the only ways of producing or consuming their respective tagged metabolites. Furthermore, reactions whose fluxes are strongly correlated can be thought of as 'glued together' by these low degree metabolites. The methods developed here could be used in predicting essential reactions and metabolic modules in other organisms from the list of metabolic reactions.